Gauss-Newton methods for robust parameter estimation
In this paper we treat robust parameter estimation procedures for problems constrained by differential equations. Our focus is on the l 1 norm estimator and Huber’s M-estimator. Both of the estimators are briefly characterized and the corresponding optimality conditions are given. We describe the so...
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| Main Authors: | , |
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| Format: | Chapter/Article Conference Paper |
| Language: | English |
| Published: |
2013
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| In: |
Model Based Parameter Estimation
Year: 2012, Pages: 55-87 |
| DOI: | 10.1007/978-3-642-30367-8_3 |
| Subjects: | |
| Online Access: | Verlag, Volltext: http://dx.doi.org/10.1007/978-3-642-30367-8_3 Verlag, Volltext: https://link.springer.com/chapter/10.1007/978-3-642-30367-8_3 
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| Author Notes: | Tanja Binder and Ekaterina Kostina |
| Summary: | In this paper we treat robust parameter estimation procedures for problems constrained by differential equations. Our focus is on the l 1 norm estimator and Huber’s M-estimator. Both of the estimators are briefly characterized and the corresponding optimality conditions are given. We describe the solution of the resulting minimization problems using the Gauss-Newton method and present local convergence results for both nonlinear constrained l 1 norm and Huber optimization. An approach for the efficient solution of the linearized problems of the Gauss-Newton iterations is also sketched as well as globalization strategies using line search methods. Two numerical examples are exercised to demonstrate the superiority of the two presented robust estimators over standard least squares estimation in case of outliers in the measurement data. |
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| Item Description: | First online: 03 August 2012 Gesehen am 15.06.2018 |
| Physical Description: | Online Resource |
| ISBN: | 9783642303678 1299336647 |
| DOI: | 10.1007/978-3-642-30367-8_3 |